Coupling planar superconducting qubits to High-overtone Bulk Acoustic Resonators (HBARs)

We propose a new planar geometry to couple superconducting qubits to High-overtone Bulk Acoustic Resonators (HBARs). Here, the qubits consist of a Nb(TiN) concentric capacitor in parallel with a Superconducting Quantum Interference Device (SQUID) made out of Al/AlO_x/Al Josephson junctions. The qubit is deposited onto a cylindrically shaped piezoelectric transducer (AlN) on top of a Sapphire or Silicon substrate. In this configuration, the qubits couple to the AlN, which in turn generate propagating phonons going into the substrate, which acts as a Phononic Fabry-Pérot cavity. This strong interaction between mechanical motion and electromagnetism, opens possibilities within the field of circuit Quantum Acoustodynamics (cQAD). Earlier work showed that the phonon lifetime is limited by diffraction losses in the substrate and thus limiting the phonon quality factor. In our work, we propose to increase this phonon quality factor by altering the substrate geometry by means of deep etching or wet etching. Doing so, we belief that we can confine longitudinal phonon modes and reduce the energy leakage due to diffraction losses and creation of transversal modes inside the substrate.